A magnet of magnetic moment M and pole strength m is divided in two equal parts, then magnetic moment of each part will be

Options

A. `M`
B. `M//2`
C. `M//4`
D. `2M`

Explanation

To solve the problem, we need to analyze the effect of dividing a magnet into two equal parts on its magnetic moment. The magnetic moment (M) of a magnet is given by the formula:

\[ M = m \times L \]

where:
- \( m \) is the pole strength,
- \( L \) is the length of the magnet.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- We have a magnet with a magnetic moment \( M \) and pole strength \( m \).
- The length of the magnet is \( L \).
- Therefore, the initial magnetic moment can be expressed as:
\[ M = m \times L \]

2. **Dividing the Magnet**:
- The magnet is divided into two equal parts. This can be done in two ways:
- **Cutting along the length**: This means we cut the magnet into two halves along its length.
- **Cutting perpendicularly**: This means we cut the magnet into two equal halves across its width.

3. **Case 1: Cutting Along the Length**:
- When the magnet is cut along its length, each part will have:
- Length of each part = \( \frac{L}{2} \)
- Pole strength remains the same = \( m \)
- The magnetic moment of each part (let's call it \( M_P \)) will be:
\[ M_P = m \times \frac{L}{2} = \frac{mL}{2} \]
- Since \( mL = M \), we can substitute:
\[ M_P = \frac{M}{2} \]

4. **Case 2: Cutting Perpendicularly**:
- When the magnet is cut perpendicularly, each part will have:
- Length of each part = \( L \) (remains unchanged)
- Pole strength of each part = \( \frac{m}{2} \)
- The magnetic moment of each part (let's call it \( M_Q \)) will be:
\[ M_Q = \frac{m}{2} \times L = \frac{mL}{2} \]
- Again, substituting \( mL = M \):
\[ M_Q = \frac{M}{2} \]

5. **Conclusion**:
- In both cases, whether the magnet is cut along the length or perpendicularly, the magnetic moment of each part is \( \frac{M}{2} \).
- Therefore, the magnetic moment of each part after division is:
\[ \text{Magnetic moment of each part} = \frac{M}{2} \]

### Final Answer:
The magnetic moment of each part after dividing the magnet into two equal parts is \( \frac{M}{2} \).

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